They share common history, they run on different operating systems. This is the part I know.
I'm interested in answers from people with comparable experience in both platforms.
Common history until 15 years ago 1994 up until SQL Server 4.21. SQL Server 6.0, 6.5 were splits. SQL Server 7 was a complete re-write and it was a truly different product to SQL Server 6.0, 6.5 which were the last of the "shared" code base.
The features are quite similar and a lot of system tables and stored procs can be run on both. However, the 2 systems don't really have much in common now except the locking strategy (as compared to Oracle or MVCC based systems).
Saying that, basic SQL is portable between the 2 and I've ported Sybase to SQL Server before.
I've also worked in/or with teams that manage both platform teams but the overlap is not as much as you expect or perhaps hope for.
Why do you ask? I wouldn't plan a career on Sybase unless you work in Banking IT...
If you stick to the ANSI SQL syntax, they are the very much the same; but they do vary, and sometimes maddeningly so.
Since each vendor wants to get you to migrate onto their platform, I would search for the how-to-migrate-x-to-y documents on their websites. They will give you a good idea of the documented differences.